Simplify the expression to a + bi form: (-5-9i)^(2) Answer:

Apply Formula: To simplify the expression (-5-9i)^(2), we need to square the complex number (-5-9i). This involves using the formula (a-bi)^2 = a^2 - 2abi + (bi)^2.Square Real Part: First, we square the real part: (-5)^2 = 25.Square Imaginary Part: Next, we square the imaginary part: (-9i)^2. Remembering that i^2 = -1, we get (-9i)^2 = 81i^2 = 81(-1) = -81.Calculate Middle Term: Now, we calculate the middle term, which is 2 times the product of the real part and the imaginary part: 2*(-5)*(-9i) = 90i.Combine Terms: We combine all the terms to get the simplified expression: 25 - 81 + 90i = -56 + 90i.

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Simplify the expression to a + bi form:

(-5-9i)^(2)
Answer:

Simplify the expression to a + bi form: $\newline$ $(-5-9 i)^{2}$ $\newline$ Answer:

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Precalculus

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Q. Simplify the expression to a + bi form:

\newline

(-5-9 i)^{2}

\newline

Answer:

Apply Formula: To simplify the expression $(-5-9i)^{2}$ , we need to square the complex number $(-5-9i)$ . This involves using the formula $(a-bi)^{2} = a^{2} - 2abi + (bi)^{2}$ .
Square Real Part: First, we square the real part: $(-5)^2 = 25$ .
Square Imaginary Part: Next, we square the imaginary part: $(-9i)^2$ . Remembering that $i^2 = -1$ , we get $(-9i)^2 = 81i^2 = 81(-1) = -81$ .
Calculate Middle Term: Now, we calculate the middle term, which is $2$ times the product of the real part and the imaginary part: $2\times(-5)\times(-9i) = 90i$ .
Combine Terms: We combine all the terms to get the simplified expression: $25 - 81 + 90i = -56 + 90i$ .